There are a fair number of common tunes where people usually expect a specific bass part, at least on the head. If you don’t play the written bass part, you’re not playing the song. For example:

All Blues

Cantaloupe Island

Chameleon

Equinox

Footprints

Giant Steps (bass follows the head through the first half)

Killer Joe

Eighty-One

Four (gotta nail those hits in the head)

Jordu (those hits again)

Milestones

Mr. PC

Nardis

A Night in Tunisia

Pent-Up House

Red Clay

So What

Song For My Father

Watermelon Man

Additionally, learn to nail the transition on tunes that switch from straight 8ths to swing 8ths. Especially if it’s a jam session or something, I usually telegraph the upcoming swing part a measure ahead with a swing fill. When the straight 8ths part is coming back, I might play a whole note for the last measure. I also find switching back and forth a little tiresome, and switch to swinging all the way through the form after we express the head. A lot of classic recordings do this too. Tunes like:

A Night In Tunisia

Caravan

Green Dolphin Street

Invitation

Love For Sale

Nica’s Dream

Old Devil Moon

And work on some of the super up-tempo tunes that you won’t be able to read on the bandstand. Memorize a coupla lines through ’em at least: